In Training 3 and First 3 the figure for the trot and for the canter IS a loop. In the walk it is not. Then it is ridden like a “VEE.” Bend coming off the track at the corner, totally straight horse out to X, briefly bend as you change direction, straight back to the “arrival letter,” and a brief bend back onto the track.
In the trot loop in T-3, the figure is ALL CURVES and the bend of the horse should change as the curve of the figure changes—at the quarter lines as you are passing S and V (or R and P).
In the First Level 3 canter loop, you ride the figure exactly the same way, BUT you don’t change the horse’s bend at all. The horse should be bent slightly in the direction of the lead he’s on throughout. Be careful not to OVERbend his neck to the inside, however. That would throw him onto his opposite shoulder. Hold the lead with your seat and leg aids, keep his withers right in front of your belt buckle, and don’t let him hang on you.
If you have a copy of the USEF Rule Book (or find it at their website online) you can find a diagram of what the loops look like in the dressage section in DR 110.